Consider a guessing game with ten players, numbered 1 through 10. Simultaneously and independently, the players select integers between 0 and 10. Thus player i’s strategy space is Si = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, for i = 1, 2, c, 10. The payoffs are determined as follows: First, the average of the players’ selections is calculated and denoted a. That is,
where si denotes player i’s selection, for i = 1, 2, c, 10. Then, player i’s payoff is given by ui = (a − i − 1)si . What is the set of rationalizable strategies for each player in this game?
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